Recovering the Designer's Ledger: Inverse Hedonic Pricing of Card Costs in a Collectible Card Game

Collectible card games (CCGs) price every card in a single integer resource, yet the rules mapping card text to cost are rarely published. We cast their recovery as an inverse hedonic pricing problem and propose ZHIZHI (Zero-residual Hedonic Inversion, Zero-shot Hedonic Imputation): Stage 1 inverts effect prices from anchor cards that differ in a single effect, so most prices are identified exactly; Stage 2 imputes any card's value from its text without refitting. The value-to-cost ratio is reported as the AMBER score (Attribute-Matched Budget-Efficiency Ratio), with 1.00 as par and repeatable triggers booked at half an activation. Applied to Riftbound, Riot Games' League of Legends card game, the framework fully prices 497 of 702 costed units and spells and 69 of 107 gear cards, extending a linear additive core with mechanism models for hand cards, selection and on-play effects. The table exposes latent design regularities: a 50% rule for repeatable contingent value (one-off conditions mostly at zero), free play-timing keywords, a 1 C same-target complementarity premium, and integer-rounding absorption of small effects on cheap units. The AMBER score has median 1.00 and interquartile range 0.86–1.07 (0.80–1.09 excluding the 146 anchor cards, at par by construction); calibrated prices predict held-out cards; and a nested ablation attributes nearly all error reduction to on-play adjustments. Booking triggers at half an activation improves prediction card by card (leave-one-out RMSE 1.541 to 1.400 C, factor fixed); its out-of-sample test is preregistered. We discuss transfer to other CCGs and use as a soft screen in procedural card generation.Version notes (v3): From model v6.1 the AMBER score books repeatable triggers at 0.5 activations (0.25 when the trigger carries an independent condition). The previous score, used in v1–v2 and in preregistered hypotheses H1–H8, is reported as the nominal AMBER score. Author order changed: Jiahao Chen (first and corresponding author), Jiaxi Catherine Lee.